The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the correction of image artifacts caused by "Maxwell terms" produced by gradient fields in MRI systems.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), some of the individual magnetic moments of the spins in the tissue align with this polarizing field. The spins also precess about the polarizing field at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins, and after the excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When exciting and receiving these signals to produce images, magnetic field gradients (G.sub.x, G.sub.y and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
It is well known that imperfections in the linear magnetic field gradients (G.sub.x, G.sub.y, G.sub.z) produce artifacts in the reconstructed images. It is a well known problem, for example, that eddy currents produced by gradient pulses will perturb the magnetic fields and produce image artifacts. Methods for compensating for such eddy current errors are also well known as disclosed, for example, in U.S. Pat. Nos. 4,698,591; 4,950,994; and 5,226,418.
It is also well known that the gradients may not be perfectly uniform over the entire imaging volume, which may lead to image distortion. Methods for compensating this non-uniformity are well known, and for example, are described in U.S. Pat. No. 4,591,789.
Other than uncompensated eddy current errors and gradient non-uniformity errors that escape correction, it can be assumed that the magnetic field gradients (G.sub.x, G.sub.y, G.sub.z) produce linear magnetic fields exactly as programmed, thus spatially encoding the NMR data accurately. With these gradients, the overall static magnetic field at location (x,y,z) is conventionally given as B.sub.0 +G.sub.x x+G.sub.y y+G.sub.z z, and the direction of the field is usually thought to be along the z-axis. This description, however, is not exactly correct. As long as a linear magnetic field gradient is applied, the overall magnetic field is nutated away from the z-axis and its amplitude exhibits higher-order spatial dependencies (x.sup.2, y.sup.2, z.sup.2, z.sup.3, . . . ). These phenomena are a direct consequence of the Maxwell equations which require that the overall magnetic field satisfy the following two conditions: .gradient..multidot.B=0 and .gradient..times.B=0. (The last equation, involving the curl of B is valid in regions where there is no true or displacement current density, which is approximately true within the object being imaged.) The higher-order magnetic fields, referred to as "Maxwell terms" (or Maxwell fields), represent a fundamental physics effect, and are not related to eddy currents or imperfection in hardware design and manufacture. Although Maxwell terms have been known for at least a decade, their effect on imaging has been largely ignored because of their minute consequence under conventional imaging conditions.
Phase contrast magnetic resonance angiograms depict vasculature by imaging flowing blood. The detection of the flowing blood relies upon the fact that an NMR signal produced by spins flowing through a magnetic field gradient experiences a phase shift which is proportional to velocity. For flow that has a roughly constant velocity during the measurement cycle the change in phase of the NMR signal is given as follows: EQU .phi.=.gamma.Mv
where M is the first moment of the magnetic field gradient, .gamma. is the gyromagnetic ratio and v is the velocity of the spins along the direction of the gradient. To eliminate errors in this measurement due to phase shifts caused by other sources, it is common practice to perform the measurement at least twice with different magnetic field gradient moments as described in U.S. Pat. No. 4,609,872. The difference in phase at any location between the two measurements is then as follows: EQU .DELTA..phi.=.gamma..DELTA.Mv
By performing two complete scans with different magnetic field gradient first moments and subtracting the measured phases in the reconstructed image, a phase map is produced which accurately measures the velocity of constantly moving spins. The accuracy of the phase map, and hence the accuracy of the angiogram, is directly related to the magnetic fields that are produced. It is known that phase errors produced by higher-order spatial gradients that necessarily result when linear magnetic field gradients are applied, can produce significant artifacts in phase contrast angiograms.